Tight tail probability bounds for distribution-free decision making

Chebyshev’s inequality provides an upper bound on the tail probability of a random variable based its mean and variance. While tight, has been criticized for only being attained by pathological distributions that abuse unboundedness underlying support are not considered realistic in many applications. We provide alternative tight lower bounds given bounded support, absolute deviation variable. obtain these as exact solutions to semi-infinite linear programs. apply distribution-free analysis newsvendor model, stop-loss reinsurance problem from radiotherapy optimization with ambiguous chance constraint.